I'm not doing anything to fix it yet. I believe the ideal solution would be to store session data in BRB's MySQL database rather than in this server's /tmp directory, which is shared by each of the sites hosted on this box (there are a few hundred), and is the likely cause of the problem.

I'm hoping that the next version of PHPBB, the forum software we use, will do this by default so I don't have to hack the current version myself. They're on Release Candidate 7 now, so I don't imagine it will be too long for the final version.

Yeah, that's fixed. I had to put a fix-er-up script in /forum/install/, and to enforce good security practices, the forum is disabled when that directory exists (I had forgotten or I would have warned everyone).